Numerical Study on the Vertical Bridgman Crystal Growth with Thermosolutal Convection

  • Park, Byung-Kyu (Department of Thermal, Fluid, and Environmental Engineering, Korea Institute of Machinery and Materials) ;
  • Kim, Moo-Geun (School of Mechanical and Automotive Engineering, Inje University) ;
  • Kim, Geun-Oh (Department of Thermal, Fluid, and Environmental Engineering, Korea Institute of Machinery and Materials)
  • Published : 2001.08.01

Abstract

A numerical analysis has been carried out to investigate the influences of thermosolutal convection on the heat and mass transfer and solute segregation in crystals grown by the vertical Bridgman technique. The governing equations are solved by a finite-volume method using the power law scheme and the SIMPLE algorithm in which body-fitted coordinate system has been used. A primary convective cell driven by thermal gradients forms in the bulk of the domain, while a secondary convective cell driven by solutal gradients forms near interface. As the solutal Rayleigh number increases, secondary cell becomes to be stronger and has a great influence on the radial concentration along the interface.

Keywords

References

  1. Carlson, F. M., Fripp, A. L. and Crouch, R. K., 1984, 'Thermal Convection during Bridgman Crystal Growth,' J. Crystal Growth, Vol. 68, pp. 747-751 https://doi.org/10.1016/0022-0248(84)90114-3
  2. Chang, C. and Brown, R. A., 1983, 'Radial Segregation Induced by Natural Convection and Melt/Solid Interface Shape in Vertical Bridgman Growth,' J.Crystal Growth, Vol. 63, pp. 343-364 https://doi.org/10.1016/0022-0248(83)90225-7
  3. Dutta, P. S., Bhat, H. L. and Kumar, V., 1995, 'Numerical Analysis of Melt-Solid Interface Shapes and Growth Rates of Gallium Antimonide in a Single-Zone Vertical Bridgman Furnace,' J.Crystal Growth, Vol. 154, pp. 213-222 https://doi.org/10.1016/0022-0248(95)00152-2
  4. Kim, C. J. and Kaviany, M., 1992, 'A Fully Implicit Method for Diffusion-Controlled Solidification of Binary Alloys,' Int. J. Heat Mass Transfer, Vol. 35, No. 5, pp. 1143-1154 https://doi.org/10.1016/0017-9310(92)90175-R
  5. Kim, M. G., 1995, 'Effects of Rotation on the Czochralski Silicon Single Crystal Growth,' Transactions of the Korea Society of Mechanical Engineers, Vol. 19, No. 5, pp. 1308-1318
  6. Kim, M. G. and Ro, S. T., 1992, 'Analysis of Solidification Process around a Vertical Tube Considering Density Change and Natural Convection,' Transactions of the Korean Society of Mechanical Engineers, Vol. 16, No. 1, pp. 142-155
  7. Kuppurao, S. and Derby, J. J., 1997, 'Designing Thermal Environments to Promote Convex Interface Shapes during the Vertical Bridgman Growth of Cadimuim Zine Telluride,' J. Crystal Growth, Vol. 172, pp. 350-360 https://doi.org/10.1016/S0022-0248(96)00756-7
  8. McFadden, G. B. and Coriell, S. R., 1987, 'Thermosolutal Convection during Directional Solidification.Ⅱ.Flow transitions,' Phys. Fluids, Vol. 30, No. 3, pp. 659-671 https://doi.org/10.1063/1.866370
  9. Ouying, H. and Shyy, W., 1997, 'Numerical Simulation of CdTe Verical Bridgman Growth,' J.Crystal Growth, Vol. 173. pp. 352-366 https://doi.org/10.1016/S0022-0248(96)00773-7
  10. Xiao, Q., Kuppurao, S., Yeckel, A. and Derby, J. J., 1996, 'On the Effects of Ampoule Tilting during Vertical Bridgman Growth: Three Dimensional Computations Via a Massively Parallel,Finite Element Method,' J.Crystal Growth, Vol. 167, pp. 292-304 https://doi.org/10.1016/0022-0248(96)00231-X
  11. Xing, Y., Tabarrok, B. and Walsh, D., 1996, 'The Influence of Thermal Convection on CdTe Growth by the Traveling Heater Heater Method,' J. Crystal Growth, Vol. 169, pp. 704-714 https://doi.org/10.1016/S0022-0248(96)00451-4